City's medical team had hoped that Mendy had just suffered an impact injury, but following the club's Champions League 2-0 victory over Shakhtar Donetsk, Guardiola gave a pessimistic prognosis.
"After tomorrow he is travelling to Barcelona and we are going to see. But I get the impression he will be out for a long time, unfortunately," the Spaniard told BBC Sport.
"It is very frustrating, firstly for him first as a person - it is very sad for him. And, for the way we want to play, we will lose a lot. It is a major set-back.
"He is a unique player. We will see in January about a new signing. We have alternatives."
Mendy joined City from Ligue 1 champions Monaco this summer for a reported £52m.